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Limits on Log Odds Ratios for Unidimensional Item Response Theory Models

Published online by Cambridge University Press:  01 January 2025

Shelby J. Haberman ,
Paul W. Holland  and
Sandip Sinharay
Shelby J. Haberman
Affiliation:
Educational Testing Service
Paul W. Holland
Affiliation:
Educational Testing Service
Sandip Sinharay*
Affiliation:
Educational Testing Service
*
Requests for reprints should be sent to Sandip Sinharay, Center for Statistical and Psychometrical Theory and Practice, Educational Testing Service, Rosedale Road, MS 12-T, Princeton, NJ 08541, USA. E-mail: ssinharay@ets.org
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Abstract

Bounds are established for log odds ratios (log cross-product ratios) involving pairs of items for item response models. First, expressions for bounds on log odds ratios are provided for one-dimensional item response models in general. Then, explicit bounds are obtained for the Rasch model and the two-parameter logistic (2PL) model. Results are also illustrated through an example from a study of model-checking procedures. The bounds obtained can provide an elementary basis for assessment of goodness of fit of these models.

Keywords

Rasch model2PL modelnormal ogive modelcumulant generating function
Type
Theory and Methods
Information
Psychometrika , Volume 72 , Issue 4 , December 2007 , pp. 551 - 561
Copyright
Copyright © 2007 The Psychometric Society

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Footnotes

Any opinions expressed in this publication are those of the authors and not necessarily those of the Educational Testing Service.

The authors thank Dan Eignor, Matthias von Davier, Lydia Gladkova, Brian Junker, and the three anonymous reviewers for their invaluable advice. The authors gratefully acknowledge the help of Kim Fryer with proofreading.

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